д) у² = 52у – 576; е) 15y² – 30 = 22y + 7; ж) 25р² = 10p – 1; з) 299x² + 100x = 500 - 101x2.

Решим уравнения:

д) $$y^2 = 52y - 576$$

$$y^2 - 52y + 576 = 0$$

$$D = (-52)^2 - 4 \cdot 1 \cdot 576 = 2704 - 2304 = 400$$

$$y_1 = \frac{52 + \sqrt{400}}{2 \cdot 1} = \frac{52 + 20}{2} = \frac{72}{2} = 36$$

$$y_2 = \frac{52 - \sqrt{400}}{2 \cdot 1} = \frac{52 - 20}{2} = \frac{32}{2} = 16$$

Ответ: y₁ = 36; y₂ = 16

e) $$15y^2 - 30 = 22y + 7$$

$$15y^2 - 22y - 37 = 0$$

$$D = (-22)^2 - 4 \cdot 15 \cdot (-37) = 484 + 2220 = 2704$$

$$y_1 = \frac{22 + \sqrt{2704}}{2 \cdot 15} = \frac{22 + 52}{30} = \frac{74}{30} = \frac{37}{15}$$

$$y_2 = \frac{22 - \sqrt{2704}}{2 \cdot 15} = \frac{22 - 52}{30} = \frac{-30}{30} = -1$$

Ответ: y₁ = 37/15; y₂ = -1

ж) $$25p^2 = 10p - 1$$

$$25p^2 - 10p + 1 = 0$$

$$D = (-10)^2 - 4 \cdot 25 \cdot 1 = 100 - 100 = 0$$

$$p = \frac{10}{2 \cdot 25} = \frac{10}{50} = \frac{1}{5} = 0.2$$

Ответ: p = 0.2

з) $$299x^2 + 100x = 500 - 101x^2$$

$$299x^2 + 101x^2 + 100x - 500 = 0$$

$$400x^2 + 100x - 500 = 0$$

$$4x^2 + x - 5 = 0$$

$$D = 1^2 - 4 \cdot 4 \cdot (-5) = 1 + 80 = 81$$

$$x_1 = \frac{-1 + \sqrt{81}}{2 \cdot 4} = \frac{-1 + 9}{8} = \frac{8}{8} = 1$$

$$x_2 = \frac{-1 - \sqrt{81}}{2 \cdot 4} = \frac{-1 - 9}{8} = \frac{-10}{8} = -\frac{5}{4} = -1.25$$

Ответ: x₁ = 1; x₂ = -1.25